I was in Botswana, South Africa, and Namibia a year ago (literally--I was there at the end of July). It's their dry season. Expect few bugs or mosquitoes. But LOTS of dust.
I know you're on a budget. My advice would be to buy two bodies and then rent two lens.
First, the minimum distance you want is going to be 400mm and if you're shooting birds to "shy" critters that you can't get close to, than 500mm or 600mm. Those lens aren't cheap. So rent one.
And then there will be times where it's low light (sunrise, sunset, blue hour periods) or a lioness walks 10 feet from your lorry and you need a 50mm that has some speed and/or a wide-open aperture. It's useful to have two bodies, one with the long lens and one that you throw in a pocket or photo vest to use when you want to shoot a person in the vehicle or an animal that is so close you can see the gnats on its' nose. I know it's tempting, really tempting to have one body and a super lens. The super lens won't cut it for this kind of photography. I'm serious--you really need a minimum of 400mm. And for birds, leopards--you're going to need to have a longer reach. If you really need to cut corners on costs, then by a teleconverter and rent a good long lens.
One of the groups I used (Pangolin) provides Nikon D7000 bodies plus 500mm zooms to anyone who needs one.
Here are a couple of other tips for you: it will be freaking cold in the morning. If it's a photo safari you'll usually be leaving before sunrise. Every morning I was wearing a boonie hat, sniper veil as a face scarf, compression t-shirt, long-sleeve t-shirt, fleece, and then a wind-breaker over it all PLUS gloves and long pants. Drivers will go fast to try and beat the crowds at the gate or once you enter a preserve.
Expect to see a ton of elephants (my first day in Botswana I stopped counting at 50--must have seen over 800 of them at least when I was there). Don't expect rhinos along the Chobe River or the Park. There is a preserve further south with Rhinos. And this time of year, the Chobe is amazing for birds. There is a nesting ground in the middle of the Chobe River for Yellow bellied Storks that is just mind blowing.
The two images below were both shot with my second body I had on this trip (a D600 with a 35-80mm zoom). The one of the lioness--that silver blur in the lower foreground is the mirror on the side of land rover. The one of the elephant--he was trying to squeeze between us and a tree. He rocked the vehicle and ripped off the driver's side mirror. So yeah, it's useful to have something that is 50mm or less.
And I have immense respect for Gary and his expertise on this subject. But I will tell you that with the combination of the dry season and lots of very dusty trails, I'd strongly suggest against swapping out lens on one body. When the vehicle was moving I wore my veil up as a mask. If you're behind another vehicle on a track you'll just be consumed by dust (even moving at about 25mph).
One other hint: I flew South Africa Airways to get to Johannesburg and then to get to Kasane in Botswana. They WILL weigh your luggage and if you're just a little bit over, but totally unforgiving. Seriously think about getting a photo vest to throw stuff in so you stay underweight with baggage, even if you don't use the vest when you shoot.